Minimal polynomials are widely used in symbolic computation. Computing the minimal polynomial of a radical expression (or more simply “radical” as used herein) is a basic problem in symbolic computation. Some examples include factorization of polynomials in an algebraic extension field, rationalization of denominators, and simplification of complex expressions.
Determining the minimal polynomial of radicals over a ring is a well known question for problems related to algebraic extension. One conventional technique used by computational software programs finds an annihilation polynomial, factors the polynomial, and then finds the minimal polynomial from the factors. However, there are drawbacks to such conventional techniques. Any improvement in computing the minimal polynomials for radicals over the ring Z of integer numbers or the field (or ring, as a field is also a ring) Q of rational numbers that improves the performance of computational software programs is thus desirable.